An optical system for a missile has optics for imaging an object through a beam path on an imaging plane. The optics have external optics, rotatably mounted about a roll axis and a pitch axis of the missile, and internal optics, and one of the ends of the beam paths is fixed with respect to the structure in the missile. In order to prevent image disturbances caused by shadows which are caused at a high squint angle by an element which is fixed to the structure, the optical system includes a shutter, which can be introduced into the beam path during flight of the missile, in order to mask out a shadow, which is produced by an element of the missile, in the beam path in a viewing direction of the external optics which is tilted with respect to the roll axis.